1,285 research outputs found
Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations
We introduce a new method, the Local Monge Parametrizations (LMP) method, to
approximate tensor fields on general surfaces given by a collection of local
parametrizations, e.g.~as in finite element or NURBS surface representations.
Our goal is to use this method to solve numerically tensor-valued partial
differential equations (PDE) on surfaces. Previous methods use scalar
potentials to numerically describe vector fields on surfaces, at the expense of
requiring higher-order derivatives of the approximated fields and limited to
simply connected surfaces, or represent tangential tensor fields as tensor
fields in 3D subjected to constraints, thus increasing the essential number of
degrees of freedom. In contrast, the LMP method uses an optimal number of
degrees of freedom to represent a tensor, is general with regards to the
topology of the surface, and does not increase the order of the PDEs governing
the tensor fields. The main idea is to construct maps between the element
parametrizations and a local Monge parametrization around each node. We test
the LMP method by approximating in a least-squares sense different vector and
tensor fields on simply connected and genus-1 surfaces. Furthermore, we apply
the LMP method to two physical models on surfaces, involving a tension-driven
flow (vector-valued PDE) and nematic ordering (tensor-valued PDE). The LMP
method thus solves the long-standing problem of the interpolation of tensors on
general surfaces with an optimal number of degrees of freedom.Comment: 16 pages, 6 figure
El sistema Archéo DATA: hacia la creación de un Sistema de Información Arqueológica
Sin resume
Analysis and Modeling of Effective Passage Retrieval Mechanisms in Question Answering Systems
A Fuzzy Time Series-Based Model Using Particle Swarm Optimization and Weighted Rules
During the last decades, a myriad of fuzzy time series models have been
proposed in scientific literature. Among the most accurate models found in
fuzzy time series, the high-order ones are the most accurate. The research
described in this paper tackles three potential limitations associated with the
application of high-order fuzzy time series models. To begin with, the adequacy
of forecast rules lacks consistency. Secondly, as the model's order increases,
data utilization diminishes. Thirdly, the uniformity of forecast rules proves
to be highly contingent on the chosen interval partitions. To address these
likely drawbacks, we introduce a novel model based on fuzzy time series that
amalgamates the principles of particle swarm optimization (PSO) and weighted
summation. Our results show that our approach models accurately the time series
in comparison with previous methods
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